# Calculation of a comet orbiting Sun

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1. May 30, 2015

### MelkoRR

1. The problem statement, all variables and given/known data
a comet is orbiting around the Sun in a parabolic orbit . center of the sun to perigee of the comet's orbit distance is 58 km .
find the time required for the comet to transit into the earth orbit around the sun .

2. Relevant equations

3. The attempt at a solution

no clue

2. May 30, 2015

### MelkoRR

i think this problem is better off in the advanced section !!

3. May 30, 2015

### Staff: Mentor

Done!

Can you clarify the phrase: "find the time required for the comet to transit into the earth orbit around the sun "? Transit from where? You need to specify the portion of the orbit involved.

Do you mean the time spent by the comet closer to the Sun than the Earth (within the orbit of the Earth)?

By the way, the quoted material is not correct when it states that the is no "eccentric anomaly" for the parabola. There is what is called the Parabolic Eccentric Anomaly, often denoted by D where

$D = \sqrt{p}~tan~\frac{\nu}{2}$

See, for example, "Fundamentals of Astrodynamics" by Bate, Mueller, and White, chapter 4.

4. May 30, 2015

### SteamKing

Staff Emeritus
You realize, of course, that at this perigee distance of 58 km from the sun's center, the comet is traveling thru the sun?!?

5. May 30, 2015

### Staff: Mentor

This thread was reported to the Mentors because you showed zero effort. But a Mentor and a retired Mentor are posting in the thread, so they will handle this.

6. May 31, 2015

### MelkoRR

my bad , it's 58 million kilometers !!

7. May 31, 2015

### MelkoRR

the problem is i don't quite understand the problem , and I've translated the problem form Persian to English . another translation that could be told is :

A comet is orbiting around the Sun in a parabolic orbit . Assuming the distance between the center of the sun to perigee of the comet's orbit is 58 million km, find the duration the comet spends in Earth's orbit.

I think the best question before any attempt for solving the problem is : "Can a comet, while staying in it's own orbit, spent some time on Earth's orbit around the sun?"

8. May 31, 2015

### Staff: Mentor

Change "in" to "within" then I would agree with this interpretation. That is, find the time that the comet spends closer to the Sun that the Earth.
Earth's orbit is an ellipse while the comet's is parabolic. They are different geometrical shapes that won't coincide for any length of time. The best that can happen is an intersect (crossing), which would happen in an instant of time.

9. May 31, 2015

### MelkoRR

exactly this is my thought , it would be a point , but the problem is asking for duration !!

so how could we find the time ?!

10. May 31, 2015

### MelkoRR

would it be possible for the comet to spend some time in earth's orbit around sun in this case ?

11. May 31, 2015

### Staff: Mentor

Well, that's what you need to work out. We can't hand you an answer here. You have to do some research and show an attempt.

I did provide a hint for a starting point: The Parabolic Eccentric Anomaly.

12. May 31, 2015

### MelkoRR

Thank you , i will post my progress here as soon as i reached somewhere !!

13. May 31, 2015

### Staff: Mentor

Again, it depends on your definition of "in". Clearly the image shows the comet's orbit spends a portion of its time within the Earth's orbit.

Note that the eccentricity of the Earth's orbit is very small so it's very close to circular. It's highly likely that you can treat it as circular for the purposes of this problem, otherwise they would have given you precise orbit details and timings to work with for both bodies.

14. May 31, 2015

### Staff: Mentor

By the way: "perigee" (the point closest to earth) should be "perihelion" (the point closest to sun) or "periapsis" (the closest point to the central object in general).